SARIMA modeling of the monthly average maximum and minimum temperatures in the eastern plateau region of India

The SARIMA time series model is fitted to the monthly average maximum and minimum temperature data sets collected at Giridih, India for the years 1990-2011. From the time-series plots, we observe that the patterns of both the series are quite different; maximum temperature series contain sharp peaks in almost all the years while it is not true for the minimum temperature series and hence both the series are modeled separately (also for the sake of simplicity). SARIMA models are selected based on observing autocorrelation function (ACF) and partial autocorrelation function (PACF) of the monthly temperature series. The model parameters are obtained by using maximum likelihood method with the help of three tests [i.e., standard error, ACF and PACF of residuals and Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and corrected Akaike Information Criteria (AICc)]. Adequacy of the selected models is determined using diagnostic checking with the standardized residuals, ACF of residuals, normal Q-Q plot of the standardized residuals and p-values of the Ljung-Box statistic. The models ARIMA (1; 0; 2) × (0; 1; 1)12 and ARIMA (0; 1; 1) × (1; 1; 1)12 are finally selected for forecasting of monthly average maximum and minimum temperature values respectively for the eastern plateau region of India.

A New Computational Method for Estimating Simultaneous Equations Models Using Entropy as a Parameter Criteria

Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.

Indian COVID-19 dynamics: Prediction using autoregressive integrated moving average modelling

Background: The forecasting of Coronavirus Disease-19 (COVID-19) dynamics is a centrepiece in evidence-based disease management. Numerous approaches that use mathematical modelling have been used to predict the outcome of the pandemic, including data-driven models, empirical and hybrid models. This study was aimed at prediction of COVID-19 evolution in India using a model based on autoregressive integrated moving average (ARIMA). Material and Methods: Real-time Indian data of cumulative cases and deaths of COVID-19 was retrieved from the Johns Hopkins dashboard. The dataset from 11 March 2020 to 25 June 2020 (n = 107 time points) was used to fit the autoregressive integrated moving average model. The model with minimum Akaike Information Criteria was used for forecasting. The predicted root mean square error (PredRMSE) and base root mean square error (BaseRMSE) were used to validate the model. Results: The ARIMA (1,3,2) and ARIMA (3,3,1) model fit best for cumulative cases and deaths, respectively, with minimum Akaike Information Criteria. The prediction of cumulative cases and deaths for next 10 days from 26 June 2020 to 5 July 2020 showed a trend toward continuous increment. The PredRMSE and BaseRMSE of ARIMA (1,3,2) model were 21,137 and 166,330, respectively. Similarly, PredRMSE and BaseRMSE of ARIMA (3,3,1) model were 668.7 and 5,431, respectively. Conclusion: It is proposed that data on COVID-19 be collected continuously, and that forecasting continue in real time. The COVID-19 forecast assist government in resource optimisation and evidence-based decision making for a subsequent state of affairs.

Modeling COVID-19 Pandemic Data with Beta-Double Exponential Model

Objective: This paper examines and upgrades a two-parameter double exponential distribution to a four-parameter beta double exponential model by compounding the baseline distribution and beta link function to fits and analyse deaths-cases data set of the recent outbreak of the global pandemic coronavirus disease (COVID-19) for both Africa and Non-Africa countries. The new proposed model, although complex in its mathematical structure, yet flexible to implement and its robustness to accommodate non-normal data is an extra advantage to statistical theory and other fields. Methodology: The statistical properties: the density function, cumulative distribution function, survival function, hazard function, moments, moments generating function, skewness and kurtosis of the developed model were presented. Maximum likelihood method is used for parameters estimation procedure. The new model is validated and compared with some frontier similar extant parametric family of beta distributions using graphs, Kolmogorov Smirnov (KS) Statistic, Log-likelihood and model criteria statistics like Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and Consistent Akaike Information Criteria (CAIC) as tools for comparison. Results: The graphs, KS, LogL and model criteria statistics values showed that the proposed model fits the COVID-19 pandemic data better than other competing models since the model has lower values as stated: The values from non-African countries KS = 0.1208, LogL = 278.4168, AIC = 560.8336, BIC = 576.1147 and CAIC = 577.1147. Also, from African countries are: KS = 0.0759, LogL = 144.0245, AIC = 292.0490, BIC = 303.9302 and CAIC = 304.9302. Conclusion: The proposed model showed its applicability and flexibility over other models considered in this work. Therefore, this implies that the new model can be used for modeling other infectious disease data and real data in many fields.

Comparative analysis of hatchability dynamics (CAHD) of eggs in selected hatcheries in Ibadan metropolis

We carried out this study to evaluate the plausibility of the representativeness of time series analysis results using egg hatchability data from 2 selected hatcheries: Bronco and Foresight hatcheries, Oluyole, Ibadan (both at Latitude 7º 23´ N and Longitude 3º 82´ E). The initial summary statistics of egg variables showed that in Bronco hatchery, the quantity of eggs set peaked (14935.53) in the months of November but lowest (11298.91) in the months of March. However, variance of eggs set in the months of September was highest (41018287) but lowest (1613430) in the months of March. The quantity of fertile eggs ranged between 10216.96 (March) and 13527.58 (November). Total number of chicks produced was highest (11966.15) in the months of November and lowest (9265.86) in the months of March. The time plot of egg set for hatching returned an unconditional cyclic variance and similarly with egg transferred. Although, total eggs hatched into chicks had different time plot pattern but it was also an unconditional cyclic variation. The Jarque-Bera (JB) statistics returned for egg set, egg transferred, total chicks hatched and ratio for Bronco hatchery are 1654.92, 1011.46, 38.721 and 57.855, respectively, while that of foresight hatchery are 25.038, 27.006, 235.897 and 365.734, respectively. The acf(x …x ) of the egg variable presented a wider value than that of acf of (x …x ) for foresight hatchery hence, the acf (x …x ) =(x …x ) could not be said to be strictly stationary. However, the acf of the x …x presented a cyclical and reducing acf like the original acf hence, (x …x ) =(x …x ). The acf of the ratio of egg set to total chicks hatched gave cyclical but reducing trend for both Bronco and Foresight hatcheries. These trends were also maintained for the x …x hence xtk+h …x = x …x . TheARIMAmodel of the ratio of the egg hatchability variables has the least corrected akaike information criteria nd Bayesian Information Criteria hence it could be adjudged the most parsimonious.